Why is Rosh Hashanah considered the Jewish New Year?

You ask a very interesting question. What actually occurred on the first Rosh Hashanah, more than 5700 years ago? What are we commemorating?

G‑d created the world in six days, and Adam and Eve, the first people, were formed on Day Six. Rosh Hashanah is the anniversary of their creation.

So why do we celebrate Rosh Hashanah, and the beginning of the year, on this day? Shouldn't it be observed six days earlier, on the anniversary of the first day of creation?

The question is strengthened when we look into the prayers of the day. During the musaf services we say "This day is the beginning of Your works, a remembrance of the first day." Is it really the first day?

The answer is that the creation of Man enables the true purpose of Creation to be fulfilled. G‑d created a world that conceals His presence, and He wants us to reveal Him. Only man — who is endowed with intelligence and freedom of choice; the ability to accept G‑d or reject Him — can accomplish this. On the day of his creation, Adam realized that G‑d is the Master of the Universe, and he said to the other creations: "Come, let us worship and bow down, let us kneel before G‑d our Maker."1

Rosh Hashanah is the day when we follow Adam's example, and accept G‑d's kingship over us and the entire world. For this is the true head of the year: the time when G‑d's goal in making the world started to be fulfilled.

Because of the significance of the day, it is the first day of the year on the Jewish calendar.

Rosh Hashanah (the first day of the seventh month) is the head of the year, while Nissan (the month in which Passover falls, is the first of the months. See Our Other Head for why this is so.
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NinaDCSeptember 24, 2014

Sorry but this thought process conveniently puts "Man" at the center of making G-d powerful and that just seems a little existentially unsound. I truly wonder what others might think ... to say that G-d is relying on us to reveal him - well, it seems kind of unhumble, and human-centric ...
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